A debate over the issue has been sparked by statements from federal Liberal candidate for Warringah Katherine Deves who published, then deleted, tweets criticising the trans community.
She compared her organisation, designed to exclude trans people from sport, to the French resistance groups during the Nazi occupation.
Ms Deves has since issued public apologies over her choice of language but Prime Minister Scott Morrison is standing by the embattled candidate.
Last Thursday Mr Kean said he believed Ms Deves should be disendorsed, saying there was no place in mainstream political parties for bigotry.
"Political leaders should be condemning the persecution of people based on their gender, not participating in it," the treasurer said.
Mr Kean stood by his comments on Wednesday, telling News Corp the language she had used was inappropriate.
"Invoking the Holocaust, one of the worst atrocities in human history, is offensive to those who lost loved ones."
Mr Perrottet said he welcomed different views within his party.
"Matt, like me, in the past, I have to be a bit careful now, likes having opinions," the premier said on Wednesday.
"You want colour and you want ideas in public life."
The premier's comments came after it was revealed he had texted Mr Morrison to reassure him of his backing over his approach to trans women in sport.
Mr Perrottet added his views on the issue were very clear.
"I think girls should play sport against girls, and women should play sport against women," he said.
He added that politicians in public life have a responsibility to engage in public debate sensitively.
"Particularly in areas that are incredibly delicate."
On Tuesday, Labor leader Chris Minns was asked on 2GB if he believed transgender people, born male, might have an advantage during sporting competitions.
"Look I think it's a complicated issue, but the simple fact is … when young male adolescents go through puberty, they have a large amount of a natural chemical called testosterone," he said.
"It's a powerful, natural, anabolic steroid and there's simply not enough preparation training, dieting or natural skill for female athletes to overcome that competitive advantage.
"It's no one's fault, it's just a problem of biology."
He said when sport bodies made decisions to ensure fairness, they should be supported.
A Labor spokesperson told AAP Mr Minns did not support the comments made by Ms Deves.
"Comparing anything to the horrific crimes of the Nazis is of course highly inappropriate and awful," the spokesperson said.
The commentary has prompted Independent member for Sydney Alex Greenwich to criticise the premier and the opposition leader and to call for calm on the issue on Wednesday.
Mr Greenwich said all MPs and candidates running for election should stop weaponising the issue of transgender and gender diverse people.
"Transgender people face significant stigma, discrimination and exclusion in the community which leads to poor mental health outcomes and high suicide rates," Mr Greenwich said.
Listening to politicians claim they posed a threat to sport and should be excluded was incredibly damaging, he added.
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